## 4. Asymmetric eclipse curve of SY MusIt is important to note that our time of mid-eclipse is not based on the light curve shape but on RV measurements. This is a crucial point because we intend to study asymmetries in the eclipse curve. ## 4.1. Column density of neutral hydrogenDuring ingress and egress we observe attenuation at wavelengths due to Rayleigh scattering and a second opacity source of up to now unknown origin. This second source of opacity has already been described in Pereira et al. (1995). In Fig. 3, we show the continuum variation at and . At 1325 Å Rayleigh scattering efficiency is very high, getting smaller towards longer wavelengths. The eclipse curve is clearly asymmetric with respect to the phase of central eclipse. At ingress a sharp flux reduction starts at . The reappearance of the hot continuum is less steep and continues until approximately .
We determine the column densities of neutral hydrogen, , with a similar approach as the one adopted by Pereira et al. (1995). We rewrite their Eq. 3 The term models an additional opacity source in a wavelength independent way, as the IUE low resolution spectra do not allow a more detailed approach. We use the spectrum SWP56762 observed at as reference spectrum . This spectrum does not yet show attenuation due to Rayleigh scattering. In addition it is least affected by nebular emission, as it is taken close to the onset of the eclipse. By fitting the ingress and egress variation with Eq. 2, we derive
the column densities and additional
optical depths (Table 5). The
error in the derived column density of neutral hydrogen is estimated
to be of the order of . At low and
high column densities the uncertainties tend to be even larger. This
error does not include systematic effects due to line blanketing
discussed in Sect. 5. For those IUE spectra we have in common with
Pereira et al. (1999), we find agreement within the error bars.
In Fig. 4 the column densities are plotted as a function of the impact
parameter The orbital inclination of SY Mus is (Harries & Howarth 1996) and the stellar separation is , or in units of the M-giant radius (Schmutz et al. 1994) .
Fig. 4 shows that the column density of neutral hydrogen in SY Mus is clearly asymmetric with respect to mid-eclipse. ## 4.2. Mass-loss rate and wind accelerationBecause the density distribution around SY Mus is not symmetric, we model the ingress and egress column densities separately with two independent, semi-spherically symmetric solutions for the volume density where is the mass-loss rate of the
M-giant, and the velocity in units
of the terminal velocity . For a
neutral wind which consists mainly of hydrogen, the mean atomic weight
is . The total column density of
hydrogen along the line of sight where We want to solve Eq. 5 for the velocity law . According to Knill et al. (1993), it is particularly advantageous to expand the function into a Taylor series as the velocity law, , is then given by with the constants recursively defined by Due to the limited orbital coverage and limited precision of the column densities, a unique determination of the velocity profile is not possible. Therefore, we reduce Eq. 7 to the first term () and one term of order . Thus we rewrite Eq. 7 into and Eq. 8 reduces to The factors ,
, and the exponent Eq. 10 requires that we know the total column density of hydrogen
as a function of impact parameter During egress of SY Mus, there is a region around where (see Fig. 5). From to , there is a sudden drop in the column density of neutral hydrogen (see Fig. 5). In the following we model this behaviour by a wind that has reached terminal velocity at , with , and is substantially ionized at impact parameters . From the sudden decrease in column density we also deduce that the transition from mainly neutral to mainly ionized hydrogen is almost instantaneous. Thus, the amount of ionized material at is negligible, and our measured column density of neutral hydrogen at is close to the total column density of hydrogen .
The first term in Eq. 10 and Eq. 11 is the dominant term for large
which yields Typical terminal velocities for M-giant winds from molecular absorption band analysis are in the range . In the following we adopt This implies a mass-loss rate for the M-giant in SY Mus of The second term in Eq. 10 and Eq. 11 is the dominant term for small impact parameters. It determines where the acceleration of the M-giant wind takes place. The best fit parameters for the second term in Eq. 10 are and (see Fig. 5). The resulting velocity profile is shown in Fig. 6.
If we assume, that for column densities , ionization becomes significant, the ingress data does not allow to derive a mass-loss rate (see Fig. 4). Assuming the mass-loss rate derived from the egress data, we find and , with large uncertainties. The wind acceleration then takes place at (see Fig. 6). © European Southern Observatory (ESO) 1999 Online publication: August 25, 1999 |